PREFACE
There is a steadily growing interest in the capabilities of
graphical methods in the field of computation and an increasing
demand for applications of these methods to a broad
spectrum of scientific and engineering formulas-scientific
principles or laws expressed in mathematical symbols.
Over the years, man's scientific endeavors have resulted
in the accumulation of ponderous volumes of these formulas
involving computation for their application to engineering
problems. At the same time, man has developed a number
of devices for reducing the labor of these computations, numerical
devices such as the abacus and tables of logarithms,
mechanical devices such as adding machines and desk calculators,
electronic devices such as the modern computer,
and graphical devices such as the slide rule and the nomograph.
It is this last class of devices with which we are now
concerned.

The calculation of a series
of values required for the solution of an engineering problem
(e.g., the design of a column for the fractionation of a hydrocarbon
mixture) can be quickly performed with all required
accuracy by the use of charts contained between the covers
of a handbook at the engineer's fingertips.

Many scientists and engineers that use graphical devices
have little idea of the relative merits and applicability of
the various types of devices, and virtually no knowledge of
the underlying theory of their construction. Yet, the mathematics
of this theory is so simple that mathematics advisers
on projects for high school science fairs would do well to
consider some of the methods described herein, such as
construction of special slide rules, nomographs for formulas
of current interest, and three-dimensional nomographs.
There is no lack of technical literature in this field, but
what is lacking is a systematic approach to the subject as
a whole, from the standpoints of both organization and
theory.

This book is an outgrowth of very earnest efforts towards
unifying my own knowledge in this field. Having made a
thorough study of nomographic methods and theory, I nevertheless
found myself in poor shape to produce a series of
nomographs based on certain polynomials describing the
characteristics of flight of helicopters.

A modification of
existing theory greatly simplified the procedure for representing
polynomials; however, it also pointed the way towards
the development of a new theory of nomographic representation,
the hyperbolic coordinate method from which have grown
generalizations and extensions covering the entire field of
nomography. At the same time, extension of the idea of the
scale equation into the areas of graph papers, graphs, and
slide rules has simplified the application of these devices in
the field of computation.

Although some topics (e.g., the hyperbolic coordinate
method of nomography) are treated in much detail because
of the lack of thorough treatment elsewhere, other topics
(e.g., graphical integration and differentiation) are recognized
as being adequately covered in other sources and are here
given only introductory discussions by way of recognizing
their family relationships.